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					Newton’s Laws
 Forces and Motion
          Laws of Motion
 formulated by Issac Newton in the
  late 17th century
 written as a way to relate force and
  motion
 Newton used them to describe his
  observations of planetary motion.
                   History
   Aristotle was an ancient Greek philosopher
   Based on his observations the common
    belief was that in order for an object to
    continue moving, a force must be exerted
    in the direction of the motion
   This lasted until Issac Newton proposed
    his “Laws of Motion” based on
    observations made of bodies free from
    earth’s atmosphere.
               Newton’s 1st Law
                         Inertia

 An object at rest will stay at rest, and
 an object in motion will stay in
 motion at constant velocity unless
 acted on by an unbalanced force.
This statement contradicted Aristotle’s teaching and was
considered a radical idea at the time. However, Newton
proposed that there was, in fact, an unrecognized force of
resistance between objects that was causing them to stop
in the absence of an applied force to keep them moving.
This new unseen resistance force became known as
“friction”.
             Newton’s 2nd Law
                       Fnet = ma

If an unbalanced force acts on a
mass, that mass will accelerate in the
direction of the force.
                                 Since 8N is greater than 2N,
  2N                  8N         the unbalanced force (6N) is to
                                 the right so the acceleration is
                                 to the right.
                  a

Newton’s 1st Law says that without an unbalanced
force objects will remain at constant velocity
(a=0)…so it seems logical to say that if we apply a
force we will see an acceleration.
             Newton’s 3rd Law
                  Action - Reaction

For every action force there is an
equal and opposite reaction force.
 Example: If you punch a wall with your fist in anger,
          the wall hits your fist with the same force.
          That’s why it hurts!



Action-reaction forces cannot balance each other
out because they are acting on different objects.
The forces acting on an object determine their
motion.
                                    Fnet
        Fnet  ma        or      a
                                     m

   Acceleration and net force are directly
    related. If Fnet doubles, acceleration doubles.

   Acceleration and mass are indirectly related.
    If m doubles, acceleration is half as much.
            A Force is…
 Measured in Newtons (N) in the
  metric (SI) system and pounds (lbs)
  in the English system
 A vector quantity requiring magnitude
  and direction to describe it
 Represented by drawing arrows on a
  diagram
                Types of Forces
     (that we will study now – there are many more)

   Weight - force of gravity
   Normal force – surface pushing back
   Friction - resistance force that opposes motion
   Applied force - force you exert, push or pull
   Tension - applied through a rope or chain
   Net force – total vector sum of all forces
   Balanced forces – equal and opposite forces
   Unbalanced forces – not equal and opposite
                 Weight
   The force of gravity acting on a mass.
        Weight always acts down!

Weight = mass (kg) * acceleration due to gravity

           Fg  W  m  g
   Weight is a force…so this is a special case
   of F=ma and the unit is a Newton.
             Mass is…
 The amount of matter in an object.
 Measured in kilograms.

 NOT a force.

 The same at any location, even on
  another planet. Not influenced by
  gravity.
            Normal Force (FN)
   Defined as the force of a surface pushing
    back on an object.
   Always directed perpendicular to the
    surface.
   This is a contact force. No contact…no
    normal force.
   NOT always equal to weight.
                  FN
Examples:                   FN   W
                                 a
                                 l
                                 l
              Table
                    Friction
   A resistance force usually caused by two
    surfaces moving past each other.
   Always in a direction that opposes the
    motion.
   Measured in Newtons.
   Depends on surface texture and how hard
    the surfaces are pressed together.
   Surface texture determines the coefficient
    of friction (μ) which has no units.
   Normal force measures how hard the
    surfaces are pressed together.
              Types of friction
   Static friction is the force an object must
    overcome to start moving.
   Kinetic friction is the force an object must
    overcome to keep moving.


         Static friction is always greater
         than kinetic friction!
Calculating the Force of Friction

                     f   FN
Where f is the force of friction, μ is the coefficient of
friction, and FN is the normal force. μ has no units!


        For kinetic friction:   f k   k FN
        For static friction:
                                f s  s FN
         May the   Net Force be with you
   Total force acting on an object
   Vector sum of all the forces
   The unbalanced force referred to in Newton’s
    Law of Motion
   Net force is equal to the mass of an object times
    the acceleration of that object.


    Fnet   F                 Fnet  ma
Net force can be found by finding
the sum of the force vectors or by
mass times acceleration.
Example using mass times acceleration:
Find the net force for a 20 kg object that
is being accelerated at 3 m/s2 .
 Fnet  ma
 Fnet  20kg (3 m s )2


 Fnet  60 N
 If acceleration is not given, use the
kinematics equations to find “a” first:

        v f  vi
  a
           t
  d  vi t    1
                   2 at 2
        vi  v f
  d                 (t )
           2
  vi 2  v f 2  2ad
Or conversely you may have to
  use the Fnet formula to get
   acceleration and then the
 kinematics equations to find
         t, d, vi, or vf.
 Finding net force using sum of the
           force vectors:
       Example 1                                             Example 2

 10 N              30 N                                      50 N

                                                                               Fnet
                   Fnet= 20 N
                                                                               =10 N
                                                             40 N
       Example 3

15 N                                                        Must draw vectors tip to
           5N                            14 N               tail first before solving:
                12 N
                                                                    Fnet
                           =                                                   14 N
7N                                                                         Ө
                2N                              7N
          6N                                                           7N

                     Fnet 2 = 14 2 + 7   2   Ө = tan-1 (14 / 7)
                       Fnet = 15.7 N            Ө = 63.4º
             Force Diagrams
   Force diagrams must include the object
    and all forces acting on it.
   The forces must be attached to the object.
   No other vectors may be attached to the
    object.
   Components of forces, axis systems,
    motion vectors and other objects or
    surfaces may be included in force
    diagrams.
   Put the mass in the object box.
                     Force Diagram
Problem: A 10 kg crate with an applied force of 100 N slides across a
        warehouse floor where the coefficient of static friction is 0.3 between
        the crate and the floor. What is the acceleration of the crate?


                                   FN

                   f = μFN                             Fapplied = 100 N
                                     10 kg




                       Weight = Fg = (10 kg)*(9.81m/s2)
               To Solve the Problem
              Now that you have the force diagram!
Problem: A 10 kg crate with an applied force of 100 N slides across a
        warehouse floor where the coefficient of static friction is 0.3 between
        the crate and the floor. What is the acceleration of the crate.

                               FN

                f = μFN
                                    10 kg
                                                      Fapplied = 100 N
                                                                         a

                   Weight = Fg = (10 kg)*(9.81m/s2)


   Write the Newton’s 2nd Law equation for the x- and y- directions.
   This time we will use both sum of forces and ma as Fnet.

           Fnet , x :  Fx  max                           Fnet , y :  Fy  ma y
           Fa  f  max                                    FN  Fg  ma y

      Now plug in what you know and solve for what you don’t.
              Solving the Problem:
Problem: A 10 kg crate with an applied force of 100 N slides across a
        warehouse floor where the coefficient of static friction is 0.3 between
        the crate and the floor. What is the acceleration of the crate.

                               FN

                f = μFN
                                    10 kg
                                                     Fapplied = 100 N
                                                                             a

                   Weight = Fg = (10 kg)*(9.8m/s2)



   Fnet , x   Fx  max                                                Fnet , y   Fy  ma y
   Fa  f  max                                                         FN  Fg  ma y
   Fa   FN  max
                                                                        FN  98 N  0
   100 N  0.3(98 N )  10kg ( ax )
                                                                        FN  98 N
   70.6 N  10kg ( ax )                                                                          Fnet   Fx  max

   ax  7.06 m s 2

				
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posted:8/29/2012
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